Background: Childhood obesity is among the leading public health challenges, worldwide. Aim: To examine the association between children’s adherence to the Mediterranean diet (MD) and weight status taking into account family structure and related behaviors. Methods: 1728 primary-school Greek students (46% males), from Athens metropolitan area, island of Crete, and the Peloponnese region, were enroled during school years 2014–2016. Children and their parents completed questionnaires which, among others, recorded family structure (i.e., married/cohabited, divorced, single parent, and widowed), dietary and lifestyle habits. Adherence to the MD was assessed through the KIDMED score (range - 4 to 12). Children’s body mass index was calculated and classified as normal, overweight/obese, according to the International Obesity Task Force classification. The working sample was 1142 children (44% males) with a recorded family structure. Results: The prevalence of overweight was 21.7% and obesity was 5.0%; overweight/obesity prevalence was higher among males than females (32.4% vs. 23.3%; p < 0.001). Overweight/obese children had a lower KIDMED score compared to normal weight (median (range): 4 (–2, 11) vs. 5 (–1, 10), p = 0.05). An inverse association between KIDMED score and children’s weight status (odds ratio (OR) (95% confidence interval (CI)): 0.95 (0.89–0.99)) was observed. Interaction between family structure and KIDMED was observed (p < 0.001); stratified analysis revealed that in children from nuclear families the KIDMED score was inversely associated with the likelihood of overweight/obesity (OR (95% CI): 0.95 (0.88–1.00)), whereas in children from single-parent families it was not (OR (95% CI): 0.94 (0.79–1.12)). Conclusion: Adherence to the MD plays a protective role against childhood overweight/obesity, particularly among children living in nuclear families.